On May 23, 20XX, the existing or current (spot) one-year, two-year, three-year, and four-year zero-coupon Treasury security rates were as follows:

₁R₁ = 4.55 percent,
₁R₂ = 4.75 percent,
₁R₃ = 5.25 percent,
₁R₄ = 5.95 percent
Using the unbiased expectations theory, calculate the one-year forward rates on zero-coupon Treasury bonds for years two, three, and four as of May 23, 20XX.

Question

Quizplus · Accepted Answer

The unbiased expectations theory suggests that the future rates can be derived from the current yield curve. To calculate the one-year forward rates for years two, three, and four, we use the formula that equates the return from investing in a long-term bond to the return from rolling over short-term bonds. The calculations are as follows:1. For the one-year forward rate one year from now (2nd year), we solve for $f_{1,2}$ in $(1 + 0.0475)^2 = (1 + 0.0455)(1 + f_{1,2})$, which gives $f_{1,2} = 4.95\%$.2. For the one-year forward rate two years from now (3rd year), we solve for $f_{2,3}$ in $(1 + 0.0525)^3 = (1 + 0.0455)(1 + 0.0475)(1 + f_{2,3})$, which gives $f_{2,3} = 6.26\%$.3. For the one-year forward rate three years from now (4th year), we solve for $f_{3,4}$ in $(1 + 0.0595)^4 = (1 + 0.0455)(1 + 0.0475)(1 + 0.0525)(1 + f_{3,4})$, which gives $f_{3,4} = 8.08\%$.

On May 23, 20XX, the Existing or Current (Spot) One-Year